Hillary Clinton again hinted that she may run for president in 2016 on Saturday night, telling an audience in Arizona she was "very much concerned" about the direction of the country and was considering “all kinds of decisions” about her future.

Following a discussion with her husband, Bill, and daughter, Chelsea, which was chaired by the talkshow host Jimmy Kimmel, Clinton was asked by a member of the audience: “Ms Clinton, if you won't represent women in politics in America as future president, who will?”

She replied: “Look, I am very much concerned about the direction of our country. And it's not just who runs for office but what they do when they get there and how we bring people together, and particularly empower young people.”

Pressed by Kimmel to give a clearer answer, she added: “I'm obviously thinking about all kinds of decisions.”

Clinton, who represented New York in the US Senate for eight years until stepping down to serve under Obama as America’s most senior diplomat, has repeatedly said she has not yet decided whether to embark on a second campaign for the White House.

Polls indicate that she would start as clear favourite in a party field that could also include vice-president Joe Biden, and would be favoured in a general election against potential Republican nominees such as Senator Rand Paul of Kentucky and the New Jersey governor, Chris Christie.

She did nothing to dampen speculation about her future earlier in Saturday's discussion, while talking about the need for people who are committed to a public cause to keep trying even when their ambitions were thwarted.

“Too many people think that somehow if they don’t get what they have worked for right away, that either they have failed or it wasn’t meant to be, or they give up because they can’t bear the energy or the disappointment of going on,” she said.

Pointing out that her husband lost his first attempt to secure political office, Clinton said she had won two elections for the US Senate and then “I had a big loss, which we all remember, and you just have to decide what you really care about”.

Singling out climate change as a problem that jeopardised the “quality of life in so many places around the world”, Clinton told Kimmel that “people are being ravaged by weather patterns and drought and so much else” due to rising temperatures.

“This generation understands much better than those that have gone before, including ours, that this is not just some ancillary issue,” she said. “I’m hoping that there will be this mass movement that demands political change … and that it becomes just as powerful as some of the other issues that decide elections here and around the world.”

Addressing an audience earlier at the event, Clinton said: “We are going to make sure the millennial generation really is the participation generation.”Asked jokingly by Kimmel whether the decisions on her future included whether she and former president Clinton, 68, would have any more children, Clinton, 66, said: “No, but I wouldn’t mind one of those grandchildren that I hear so much about.”

Describing her mother as “shameless, shameless”, Chelsea, 34, hailed her “unapologetic pressure, in public and private”.